math.square on complex, imaginary part

Average Error: 0.1 → 0.1

Time: 4.9s

Precision: 64

Math

\[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]

↓

\[\left(\mathsf{qma}\left(\left(\left(re \cdot im\right)\right), im, re\right)\right)\]

C

double f(double re, double im) {
        double r10194 = re;
        double r10195 = im;
        double r10196 = r10194 * r10195;
        double r10197 = r10195 * r10194;
        double r10198 = r10196 + r10197;
        return r10198;
}

↓

double f(double re, double im) {
        double r10199 = re;
        double r10200 = im;
        double r10201 = r10199 * r10200;
        double r10202 = /*Error: no posit support in C */;
        double r10203 = /*Error: no posit support in C */;
        double r10204 = /*Error: no posit support in C */;
        return r10204;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.1

   \[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]
2. Using strategy rm

3. Applied introduce-quire 0.1

   \[\leadsto \frac{\color{blue}{\left(\left(\left(re \cdot im\right)\right)\right)}}{\left(im \cdot re\right)}\]

4. Applied insert-quire-fdp-add 0.1

   \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\left(re \cdot im\right)\right), im, re\right)\right)}\]

5. Final simplification 0.1

   \[\leadsto \left(\mathsf{qma}\left(\left(\left(re \cdot im\right)\right), im, re\right)\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))